Assume that we want to carry out an experiment with v+1 treatments in lock with common block-size k. Here we concentrate on generalized least-squares estimation for a known correlation structure. We consider approximate design and determine an optimal approximate design. This method may lead to exact optimal designs for some v,b,k but usually will only indicate the structure of an efficient design for any particular v, b, k, and yield an efficiency bound, usually unattainable. The bound and the structure can then be used to investigate efficient finite designs. We assume within-block correlations are the assume for each block, and errors in different blocks are uncorrelated. We consider the case where there is a control-treatments 0, say, and v test-treatments and we are interested in comparing the test-treatments with the control. Some methods of searching for highly efficient design are proposed for situations in which it is difficult to determine an A- optimal design. We suggest an algorithm to obtain A- optimal incomplete block designs for any value of v,b and k and for any type of correlations.